How can you use the greatest common factor to find the simplest form?

Answer 1

To simplify or reduce an improper fraction, you can divide the numerator and denominator by the greatest common factor of both numbers. For example, if you are given the fraction

36/60; the common factors of the numerator (36) are 2, 3, 4, 6, 9, 12, and 18. The common factors of the denominator are 2, 3, 5, 6, 10, 12, and 20. We can see that 12 is the largest common factor between the numerator and denominator.

Divide the numerator and denominator by 12: 36 / 12 = 3, and 60 / 12 = 5. We see that the fraction reduces to

3/5.

Answer 2

The greatest common factor (GCF) is a factor that divide 2 or more numbers.

To make this understandable, the example is provided:

Find the GCF of 4 and 8. Factor out each term to get:

4 = 2²

8 = 2³

Note that 4 and 8 have 2²'s in common. Select 2², and that is the GCF of the term.

Once you've found the GCF, divide that number into both the numerator and the denominator. The result will be the simplest form of the fraction. For instance,

4 / 8 = 2² / 2³ = 2² * 1 / (2² * 2) 1 / 2

Divide each term by 2² to simplify the fraction!

Answer 3

The least common factor of any set of numbers is 1, so that doesn't help at all. Finding the GCF of the numerator and denominator and dividing them by it will help to simplify a fraction. Finding the least common multiple of the denominators (called the least common denominator) will help when you add and subtract fractions. None of those are needed to multiply fractions.

Answer 4

That depends on what you want to do with them. Since fractions aren't equations, they don't need to be "solved." Sometimes they need to be reduced. To do that, find the GCF of the numerator and denominator and divide them both by it. If the GCF is 1, the fraction is in its simplest form. Sometimes unlike fractions need to be added and subtracted. To do that, find the LCM of the denominators and convert them to like fractions.

Answer 5

After you're done multiplying, the GCF will help you determine the simplest form of the answer.

Answer 6

Divide the GCF into the numerator and denominator. The result will be the simplest form of the fraction.

Example: 30/42

The GCF is 6.

The simplest form is 5/7